56 PROCEEDINGS OF THE AMERICAN ACADEMY. 



or of equal simplicity containing the fugacit}' instead of the vapor 

 pressure. Let us proceed to the determination of the laws according 

 to which fugacity changes with changes in the variables upon which 

 the condition of a substance depends, considering in the present paper 

 only those systems which are composed of a single chemically simple 

 substance. 



III. 



Influence of Temperature and Pressure on the Fugacity. 



Let us consider two phases of a substance at the same temperature 

 and pressure, but not necessarily in equilibrium with each other. A 

 solvent may be chosen in which both phases are soluble without molecu- 

 lar change, and to so slight an extent that the saturated solutions may 

 be regarded as infinitely dilute. In such a case the solubility of each 

 phase is governed by the following equation, which may be obtained 

 directly from equations (2) and (3), 



'51nn\ Q 



"^1 



RT' 



in which 11 is the osmotic pressure of the saturated solution and Q the 

 reversible heat of solution (that is, inclusive of the osmotic work). We 

 may write for the two phases, 



^1 - ^2 (9) 



/ TT ^ 



V 



9 T 



RT' 



Q^ — Q„ may be conveniently replaced in the following way. Let one 

 gram-molecule of the first phase be dissolved in the solvent, this solution 

 then diluted or concentrated to the osmotic pressure lis, and then the 

 gram-molecule removed as the second phase. If these three steps be 

 done reversibly the heat absorbed in each will be respectively 



lJ-2 



The total heat change is a function only of the conditions of the two 

 phases, not of the path by which one passes into the other, and may be 

 designated by ^1,2, thus, 



